Determine Vertical Shifts - Trigonometry
Card 0 of 7
Let 
be a function defined as follows:
The 4 in the function above affects what attribute of the graph of 
?
Let
The 4 in the function above affects what attribute of the graph of
The period of the function is indicated by the coefficient in front of 
; here the period is unchanged.
The amplitude of the function is given by the coefficient in front of the 
; here the amplitude is -1.
The phase shift is given by the value being added or subtracted inside the 
function; here the shift is 
units to the right.
The only unexamined attribute of the graph is the vertical shift, so 4 is the vertical shift of the graph. A vertical shift of 4 means that the entire graph of the function will be moved up four units (in the positive y-direction).
The period of the function is indicated by the coefficient in front of
The amplitude of the function is given by the coefficient in front of the
The phase shift is given by the value being added or subtracted inside the
The only unexamined attribute of the graph is the vertical shift, so 4 is the vertical shift of the graph. A vertical shift of 4 means that the entire graph of the function will be moved up four units (in the positive y-direction).
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Let be a function defined as follows:
What is the vertical shift in this function?
Let
What is the vertical shift in this function?
The period of the function is indicated by the coefficient in front of ; here the period is unchanged.
The amplitude of the function is given by the coefficient in front of the ; here the amplitude is 3.
The phase shift is given by the value being added or subtracted inside the cosine function; here the shift is units to the right.
The only unexamined attribute of the graph is the vertical shift, so -3 is the vertical shift of the graph. A vertical shift of -3 means that the entire graph of the function will be moved down three units (in the negative y-direction).
The period of the function is indicated by the coefficient in front of
The amplitude of the function is given by the coefficient in front of the
The phase shift is given by the value being added or subtracted inside the cosine function; here the shift is
The only unexamined attribute of the graph is the vertical shift, so -3 is the vertical shift of the graph. A vertical shift of -3 means that the entire graph of the function will be moved down three units (in the negative y-direction).
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This graph shows a translated cosine function. Which of the following could be the equation of this graph?
This graph shows a translated cosine function. Which of the following could be the equation of this graph?
The correct answer is 
. There are no sign changes with vertical shifts; in other words, when the function includes 
, it directly translates to moving up three units. If you thought the answer was 
, you may have spotted the y-intercept at 
and jumped to this answer. However, recall that the y-intercept of a regular 
function is at the point 
. Beginning at 
and ending at 
corresponds to a vertical shift of 3 units.
The correct answer is 
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The graph below shows a translated sine function. Which of the following functions could be shown by this graph?
The graph below shows a translated sine function. Which of the following functions could be shown by this graph?
A normal 
graph has its y-intercept at 
. This graph has its y-intercept at 
. Therefore, the graph was shifted down three units. Therefore the function of this graph is 
.
A normal 
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Consider the function 
. What is the vertical shift of this function?
Consider the function 
The general form for the secant transformation equation is 
. 
represents the phase shift of the function. When considering 
we see that 
, so our vertical shift is 
and we would shift this function 
units up from the original secant function’s graph.
The general form for the secant transformation equation is 
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Which of the following is the graph of 
with a vertical shift of 
?
Which of the following is the graph of 
The graph of 
with a vertical shift of 
is shown below. This can also be expressed as 
.
Here is a graph that shows both 
and 
, so that you can see the "before" and "after." The original function is in blue and the translated function is in purple.
The graphs of the incorrect answer choices are 
(no vertical shift applied), 
(shifted upwards instead of downwards), 
(amplitude modified, and shifted upwards instead of downwards), and 
(shifted downwards 3 units, but this is not the correct original graph of simply 
since the amplitude was modified.)
The graph of 
Here is a graph that shows both 
The graphs of the incorrect answer choices are 
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Which of the following graphs shows one of the original six trigonometric functions with a vertical shift of 
applied?
Which of the following graphs shows one of the original six trigonometric functions with a vertical shift of 
We are looking for an answer choice that has one of the six trigonometric functions, as well as that function shifted up 3 units. The only answer choice that displays that is this graph of 
(purple) and 
(blue).
The incorrect answers depict 
and 
, 
and 
, and 
and 
.
We are looking for an answer choice that has one of the six trigonometric functions, as well as that function shifted up 3 units. The only answer choice that displays that is this graph of 
The incorrect answers depict 
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